In recent times, dynamic boundary conditions which also exhibit a Cahn–Hilliard type structure have become very popular, especially since they allow for a better description of the transfer of material between bulk and surface (see, e.g., [1]}). In these models, the boundary condition () is replaced by a Cahn–Hilliard type equation on the surface, that is
\(&\partial _{t}\psi = \textnormal {div}_\Gamma \big ( m_\Gamma (\psi ) \nabla _\Gamma \theta \big ) - \beta m_\Omega (\psi )\, \partial _\mathbf {n}\mu &&\quad \text{on $\Sigma $},\\[1ex]&\theta = - \delta \kappa \Delta _\Gamma \psi + \delta ^{-1} G^{\prime }(\psi )+ \varepsilon \partial _\mathbf {n}\phi &&\quad \text{on $\Sigma $}.\) 
